Zero Point Energy and Relativity

Scientific Paper
Title	Zero Point Energy and Relativity
Read in full	Link to paper
Author(s)	Barry John Setterfield
Keywords	Zero Point Energy, General Relativity, Einstein, Vacuum, ZPE, Stochastic Electrodynamics, polarizable vacuum, varying constants
Published	2012
Journal	Proceedings of the NPA
Volume	9
No. of pages	21
Pages	528-548

Read the full paper here

Abstract

A wide-ranging review of the origins and successes of Relativity, both Special and General, is undertaken. The Michelson-Morley (M-M) experiment is briefly examined and the properties of the "ether" that this suggested is noted. These properties are then re-examined in conjunction with a developing branch of physics, Stochastic Electro-Dynamics (SED). SED physics emphasizes a real, not virtual, vacuum Zero Point Energy (ZPE). Our knowledge of how the vacuum ZPE behaves fulfils all the criteria required by the M-M experiment. Furthermore, it is shown that the main predictions of Einstein's Special and General Relativity easily emerge using SED physics and the ZPE. These results are obtained with simple mathematics and intuitive concepts rather than the elaborate reasoning and difficult equations that Einstein required. A deeper understanding of the nature of mass and gravity emerges from the SED equations, along with some insights into gravity waves and their speed. A suggested explanation, involving both the SED approach and plasma physics, is given for the lack of gravitational lensing of stars near the object at the center of our galaxy.

Overview

Barry Setterfield's thesis is that relativity was an unnecessary detour. The 1887 Michelson–Morley null result left three options: change the properties of matter (FitzGerald and Lorentz), change the properties of space and time (Einstein), or conclude that the ether simply has properties different from those assumed. Setterfield argues for the third, and identifies the real medium with the vacuum zero-point energy as treated in Stochastic Electrodynamics (SED) — the programme descending from Planck's neglected "second paper" of 1911, revived by de Broglie in 1962, and developed by Timothy Boyer, Hal Puthoff, Bernard Haisch and Alfonso Rueda.

The paper's method is to take each celebrated success of special and general relativity in turn — the null ether-drift result, relativistic mass increase, clock slowing, E = mc², the deflection and delay of light, the Mercury perihelion advance, frame dragging, gravitational waves, lensing — and produce it from a real, mechanical ZPE with, in Setterfield's repeated phrase, "simple mathematics and intuitive concepts". The strong extra claim, which separates this paper from ordinary SED work, is that the strength of the ZPE has changed over time, so that h and c are not constants but inversely coupled variables with hc = const. This connects the paper to Setterfield's long-standing c-decay programme and to its companion in the same proceedings, The Zero Point Energy, Light and Time.

The argument

The ZPE as the real ether

The zero-point field is described as electromagnetic waves of all wavelengths, present even at 0 K, with a frequency-cubed spectrum cut off at the Planck length of 10⁻³⁵ m. Setterfield lists the standard evidence: liquid helium cannot be frozen by cooling alone, irreducible noise in microwave receivers, the Lamb shift, and the Casimir effect.

The key property is drawn from Boyer: the cubic spectrum "is the same for all unaccelerated observers, no matter what their velocity; moreover, it is the only spectrum that has this property," because the Doppler shift in frequency is exactly compensated by the shift in intensity. The ZPE is therefore Lorentz invariant, and uniform motion through it is undetectable — though acceleration is, via the Davies–Unruh effect, at accelerations of order 10²¹ g.

A second, local mechanism is offered. ZPE waves jiggle the massless charged point particles Feynman called "partons"; the jiggling charges radiate a secondary field which boosts the ZPE locally around massive bodies. This augmented field is co-moving with the Earth's centre of mass, so an interferometer at rest on Earth sees no fringe shift — while the Earth's rotation relative to that field does produce shifts, which Setterfield identifies with the Sagnac effect (1913) and the Michelson–Gale experiment (1925).

Variable light speed and the hc invariant

The chain that carries the rest of the paper is short. In Planck's second theory h measures the strength of the ZPE, so h ~ U. A denser ZPE means more virtual pairs per unit volume (Setterfield quotes 10⁴² per cubic metre), each of which briefly absorbs and re-emits a passing photon, so light is slowed: c ~ 1/U. Together these give hc = constant. Since ε and μ also scale with U and c² = 1/εμ, the whole set is consistent. Because the ZPE is uniform at any instant, c is the same in all directions — the Michelson–Morley result — but not necessarily the same at all times.

Setterfield claims the historical measurement record supports this: h and atomic masses rising and c and atomic clock rates falling until 1970, then reversing, which he reads as the oscillation of a static cosmos of the kind Arp and Narlikar showed to be stable against collapse. Wavelengths are held fixed throughout, so f ~ c and no refraction accompanies a cosmological ZPE change.

Mass, and why relativistic mass increase follows

Mass, in this picture, is not intrinsic. The Haisch–Rueda–Puthoff formulation makes the atomic mass of a parton m ~ Γhω²/2πc², where Γ is the Abraham–Lorentz damping constant and ω = 8π²f the Zitterbewegung frequency — the jitter Schrödinger named and Dirac showed to occur at nearly the speed of light, and which Setterfield notes was demonstrated experimentally with calcium ions in 2010. A particle in motion runs into more ZPE waves, jiggles harder, and gains mass; the effect is quantified in SED and, Setterfield says, "yields the same results as relativity."

Clock slowing follows from conservation of atomic kinetic energy: if m ~ 1/c² and ½mv² is constant, then v ~ c ~ f ~ 1/U. Slower subatomic velocities mean slower atomic processes, hence slower clocks and slower radioactive decay for accelerated particles — the same prediction as special relativity but from a stated mechanism.

Alongside atomic mass Setterfield introduces an intrinsic mass m* of purely electromagnetic origin, m* ≈ e²/4πεr₀c². Balancing Puthoff's outward Coulomb energy W_Coul ~ 1/r₀ against the inward vacuum energy W_vac gives r₀ ~ 1/U⁴ and hence m* ~ c², exactly inverse to m. The product m m* = M² is therefore constant, and M is identified with gravitational mass. Working through the Haisch–Rueda–Puthoff relation m = 4παm_p²/3m* with the fine structure constant and the Planck mass, Setterfield derives that G is a genuine constant and that GM is invariant — so planetary orbit periods are untouched by a changing ZPE.

Gravity as vacuum polarization

Gravity is taken from the polarizable-vacuum account of Puthoff, Haisch and Rueda: oscillating charges polarize the charged virtual pairs of the vacuum in alternating layers, and the polarized vacuum then acts on charges in a second body, "which might explain why gravity is so weak" since one mass never pulls directly on another. Setterfield adds the argument that gravity does not change as the ZPE changes: the polarization due to charge alone is fixed because e²/ε is constant, and the extra polarization from jitter is exactly cancelled by the slower ZPE waves being less able to accelerate the partons.

The geometric alternative is rejected on causal grounds. Quoting Pushing Gravity and Haisch's group, Setterfield presses the familiar objection to the rubber-sheet picture: "why would a small particle placed at rest in that manifold begin to move towards the source mass? ... However successful this geometric interpretation may be as a mathematical model, it lacks physics and a causal mechanism."

Light bending, Shapiro delay, and the perihelion of Mercury

Here the paper leans on Eddington's own 1920 remark that the gravitational effect on light can be imitated "precisely" by a refracting medium of index n = 1/(1−2φ/r), so that ray paths follow from geometrical optics. Setterfield argues the augmented ZPE is exactly that medium: it thickens near mass, its potential falls as 1/r, and it slows light in proportion to its strength, giving n = U/U₀ = 1/(1−2φ/r). Bending arises from wavefronts bunching at the interface — a local effect — whereas a cosmological ZPE change slows the whole wave train at once and produces no refraction. The Shapiro radar delay follows from the same slowing.

For Mercury, Setterfield adopts Van Flandern's observation that perihelion motion is generically an integer multiple of a basic form N = μn/c²a(1−e²), and that general relativity assembles the observed 3N from three separate contributions (+4N time dilation, −2N space contraction, +N mass increase) — "curious that Einstein required a combination of three effects, with one of them cancelling 40% of the contribution of the other two." The ZPE model has no time dilation and no space contraction to draw on. Instead the planet is retarded as it ploughs through the thicker cloud of virtual particles near perihelion, equivalently as its de Broglie matter waves slow in the denser medium. Carrying the resulting velocity perturbation through Danby's perturbation equations and Kepler's third law yields dω/dt = 3N, which Setterfield computes as 42.98" per century — "well within the 1% measurement error mentioned by Van Flandern."

Frame dragging, gravitational waves, and the speed of gravity

Lense–Thirring precession is reinterpreted as a viscous torque: a spinning body orbiting through the dense virtual-particle cloud near a mass experiences a resistance that precesses its spin axis, as with a spinning top. Setterfield accepts that Gravity Probe B confirmed general relativity to 10% and argues the ZPE account reproduces it without "the complicated dragging of rubbery space-time." Gravitational waves become long-wavelength electromagnetic bow waves in the virtual-pair medium, generated by any orbiting body. The speed of gravity is not tied to c: gravity propagates as vacuum polarization, which is not impeded by the virtual particles that slow light, so Setterfield endorses Van Flandern's estimate of order 10¹⁰ times the current c — possibly the original speed of light before the ZPE built up.

Lensing, dark matter, and Sagittarius A*

Lensing needs only a dense concentration of matter producing enough Zitterbewegung secondary radiation to thicken the local vacuum; the gravitational field as such does nothing. Setterfield takes the shortfall of observed lenses, and cases where the visible mass appears insufficient, as evidence against the geometric account, and rejects the 400 trillion solar masses of dark matter invoked for Abell 2218. Citing Anthony Peratts plasma simulations of galaxy rotation and Dowdye's work on solar-limb light bending, he proposes that the arcs and rings are images formed at the double layer of a plasma filament seen end-on.

The final section is the paper's boldest observational claim. Twenty-eight stars have been tracked around Sagittarius A*, whose orbits imply a point mass of about 3 million suns; yet, on Dowdye's account, two decades of intense observation "have revealed not a shred of evidence for any gravitational lensing" there. Setterfield concludes the object may not be a black hole at all but a plasmoid at the focus of the galactic current circuit, and writes Peratt's equation of motion m dv/dt = mg + q(E + v×B) − νv + F, arguing that with mg negligible the electromagnetic terms must supply the observed stellar accelerations.

Assessment

The paper's genuine contribution is its insistence on mechanism. On every point where general relativity offers a geometric description, Setterfield asks what physically does the work, and the demand is legitimate: the rubber-sheet analogy really is circular as usually told, and Haisch's observation that geodesics tell you the free path but not why a force appears when you leave it is a fair criticism of how the theory is taught. The optical-medium reformulation of light bending is not a fringe move either — it is Eddington's own, and de Felice catalogued nine authors who pursued it. The ZPE identification is likewise well chosen: a Lorentz-invariant frequency-cubed field is exactly the kind of medium that could survive Michelson–Morley, and Boyer's uniqueness result is real. The mass-from-jitter account is a serious research programme with published mathematics behind it, not an invention of this paper, and Setterfield is careful to attribute it.

The difficulties begin where the paper's own additions start. The claim that h and c have measurably varied, with a reversal in 1970, rests on a reading of the historical record of recommended values that the metrological community attributes to improving technique and shifting systematic errors, not to a changing constant — and since 1983 c has been defined as exactly 299,792,458 m/s, so a "measured" drift after that date is not available even in principle. Independent bounds cut the other way: the Oklo natural reactor and quasar absorption-line studies constrain any drift in the fine structure constant to parts in 10¹⁷ per year, and the paper's own claim that α = v/c is exactly invariant is asserted from the proportionality v ~ c rather than tested against those measurements. Setterfield's response — "go with the data or go with the theory" — is the right instinct applied to the wrong data set.

Several derivations are chains of proportionalities rather than derivations. The route from W_vac to r₀ ~ 1/U⁴ and thence to m* ~ c² depends on substituting three separate U-scalings into an integral and reading off an exponent; the constants of proportionality, which is where such arguments usually fail, are never carried. The factor-of-2 discrepancy between inertial and gravitational mass in the Haisch–Rueda–Puthoff equation is disposed of by multiplying the right-hand side by 2 because the answer requires it — the paper says so plainly. The Mercury calculation is the strongest quantitative section and does arrive at 42.98"/century, but the retarding force is introduced by analogy ("ballistically through a thick cloud of virtual particles"), and a real drag on a planet would be dissipative and would decay the orbit, which is not addressed.

Two empirical claims are more exposed than the paper allows. First, the assertion that length contraction "has never been seen directly in any experiment" is at odds with the routine engineering of relativistic beams — the transverse field compression of ultrarelativistic bunches in colliders is measured, and heavy-ion collision geometry is modelled with contracted nuclei. Second, and more seriously, the Sagittarius A* argument has aged badly: the Event Horizon Telescope published a resolved image of the Sgr A* emission ring in May 2022, and the GRAVITY interferometer detected the general-relativistic gravitational redshift of S2 at pericentre in 2018 and the Schwarzschild precession of its orbit in 2020. Those results were not available in 2012 and the paper cannot be faulted for not knowing them, but they now bear directly against the plasmoid alternative, and the specific complaint about missing lensing near Sgr A* has largely been overtaken by direct imaging of the shadow.

Finally, the paper is a survey rather than an argument, and its breadth is bought at the cost of depth. Thirteen distinct relativistic phenomena are addressed in twenty-one pages, several of them — gravitational waves, the speed of gravity — in a few paragraphs of qualitative analogy. Where the ZPE account differs numerically from general relativity, as it must for a speed of gravity 10¹⁰c, no test is proposed to distinguish them. The programme deserves the serious consideration Setterfield asks for, but it would be better served by one calculation carried through with constants than by thirteen reproduced by proportionality.